Monte Carlo study of the XY-model on Penrose lattices

Journal of Physics Condensed Matter

Volumn 10, Issue 10, 1998, Pages 2303-2321

  Reid, R W ^a   Bose, S K ^a   Mitrovic B ^a  

^a BROCK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006251324     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/10/10/012     Document Type: Article

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33. We estimated the slope towards the rightmost sections of the curves. Given the error bars in the results and the mesh size, these are crude estimates. We do find that the slope P ∼ A ln(N), with A lying between 0.25 and 0.26. There is a small intercept, but considering the uncertainties in our estimates of P for the four N-values, we consider this as a fair indication that the slope goes to infinity in the thermodynamic limit. Since the slopes refer to the parts of the curves before the zero value of the helicity modulus is reached, we infer that the drop is discontinuous in the thermodynamic limit. However, since we have only four data points over a range of N which is admittedly narrow on the logarithmic scale, the above conclusion stands on shaky grounds. The magnitude of the discontinuity also remains uncertain.
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